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I have no idea why (maybe because I am reading Brave Story and watching FLCL at the same time) but I would really like some suggestions for these kinds of anime.

Completely off the wall:
You know what I mean! Anime that is just made of "what the hell did I just watch?" or "mind screw" like FLCL, Magical Shopping Arcade Abenobashi (this is a double hitter with what I ask), Sayonara Zetsubou Sensei, and the much darker "disturbing mind screw" of Higurashi.

Going to another dimension:
What it says on the tin here. Fushigi Yuugi and the like.

For something completely off the wall, I'd say Paprika is absolutely perfect for what you're looking for. I'd also have to recommend Summer Wars and Baccano!. If you liked Sayonara Zetsubou Sensei then you may like other anime produced by Shaft such as Bakemonogatari and Arakawa Under The Bridge.

Puni Puni Poemi falls under the category of "What the hell did I just watch?"

Paranoia Agent is very screwy too.

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Seto no Hanayome is a really over the top comedy with a lot of scenes that might you laugh, go WTF?, or both at the same time. The pinnacle of this is the last episode, which has to be seen to be believed.

If you're okay with manga, there's Jojo's Bizarre Adventure, which lives up to its title especially from Part 3 onwards. It's one of the strangest action series I've ever seen with numerous bizarre and creative fight scenes like a chase scene where the hero on a motorbike races tries to find the villain attacking him while being pursued by energy draining feet sent by the villian at 60 miles per hour or an epic Rock Paper Scissors match that involves glass being shattered, a boy nearly getting hit by a truck, and people soaring in the air (it makes sense in context)

For a darker take on the whole going to another dimension/world concept, there's Now and Then, Here and There. Don't be fooled by the first episode, the show reveals its true nature halfway into the 2nd episode.

Off the Wall:Neon Genesis Evangelion. I mean seriously. You deserve some kind of medal if you can decipher the ending. I got depressed trying to figure it out.Revolutionary Girl Utena - Well I was confused as hell at the plot anyway.Suzumiya Haruhi no Yuutsu - On the surface it's good comedy. But then, comes Espers, Time Travel Holes, and Alien Overminds, and while the characters themselves explains things, you'll be like... wut?

Both:Tsubasa - Resevoir Chronicle - The heroes dimension hop in order to retrieve the memories of one of their companions. It starts out simple enough, but then the plot becomes so freaking convoluted as every character and their mother seems to be plotting something on somebody else at the same time, which makes even the characters wonder WTF is going on. Combine this with alternate dimensions and you see what I'm getting at.

Gintama...if you exclude the action drama arcs, 70% of the anime is made of WTF. Seconding Excel Saga, adding Bokusatsu tenshi Dokuro-chan - WARNING: contains high levels of violence and gore...in a funny way though.

With a title like Mind Game, that movie screws you over and leaves you wondering if you should try starting a marijuana habit just to see if it gets even better than it is when you're high and off-the-wall yourself.

don't take that too seriously now

Just so you know Masaaki Yuasa -- its director -- is also the mastermind behind this season's Tatami Galaxy (already recommended), which means you should google him and watch all the stuff in his repertoire for more off-the-freaking-4th-dimension-wall than the average human can handle in a day.